This slide shows data for two product options; one with no linearization and one for the MAX31856 with on chip linearization. This clearly shows how much more work the engineer has to do if they want to write their own linearization firmware (and how little has to be done if the engineer uses the MAX31856). The largest nonlinearities for a Type K thermocouple are below 0°C and above 1000°C and that the error with no linearization can be between 15 to 60oC, while the MAX31856 is less than ±0.05oC due to the internal linearization.